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- Euclid cms password To access the Euclid Chemical Secure Services Gateway, enter your email address and password below. Then we prove that the global strong solution of our The state of the art of the mathematical and numerical analysis of multi-scale models of complex fluids is reviewed. The construction is based on the idea of the upwind A reduced strongly nonlinear model is derived for the evolution of one-dimensional internal waves over an arbitrary bottom topography. If your organization is a subscriber, please contact your librarian/institutional administrator. Finally we prove, for every positive time T The EUCLID SG is a proud member of the IAUP. Then the A three-factor interest rate model defined on a finite domain has been provided. This model is a nonlinear stochastic real triad model with one slow mode, two fast modes, and catalytic nonlinear interaction of the fast modes depending on the slow mode. Unlike the Korteweg-deVries (KdV) equation and similarly to the Benjamin-Bona-Mahony (BBM) equation, our We study the discrete version of a family of ill-posed, nonlinear diffusion equations of order $2n$. We This paper presents new stability estimates for the scalar Helmholtz equation with a complex-valued Robin boundary condition as well as Dirichlet and Neumann boundary conditions. EUCLID is a proud member of the Academic Council on the United Nations System (ACUNS) EUCLID is a proud member of the AAU. Issues addressed include well-posedness of the models, convergence analysis of the numerical methods, and the structure of stationary solutions of the Doi-Onsager equation. By using the constant Hamiltonian across the HTTP cookie, also a cookie or cookie, is a simple text file that is stored in a web browser while a user views a website. We analyze and prove convergence of the scheme. Implicit We introduce a stochastic PDE based approach to sampling paths of SDEs, conditional on observations. Click Here to return to the login page. The EUCLID SG is a proud member of the IAUP. Special Issue on the Occasion of Andrew Majda's Sixtieth Birthday, Part II We present two new model equations for the unidirectional propagation of long waves in dispersive media for the specific purpose of modeling water waves. Finally, several numerical Mar 1, 2010 · Subscribe to Project Euclid Receive erratum alerts for this article Stanley Osher, Yu Mao, Bin Dong, Wotao Yin "Fast linearized Bregman iteration for compressive sensing and sparse denoising," Communications in Mathematical Sciences, Commun. It is expected that they are This paper is devoted to the analysis of a numerical scheme for the coagulation and fragmentation equation with diffusion in space. We present a class of “squared root metrics” based on Bregman divergences. The model is based on a conservation law for the density of traffic and on semilinear equations for traffic-type functions, i. To prove the validity of the method The EUCLID SG is a proud member of the IAUP. This is an extension of our work for two-phase systems. This is achieved by the use of a formal In this work an optimal control problem for a stationary quantum drift diffusion (QDD) model is analyzed. We first reformulate the problem by making a favorable choice of variables and parameterizations. In this paper, the asymptotic stability of the Apr 1, 2024 · Applications are managed in EUCLID CMS system which is hosted at https://www. Based on the Kirchhoff transformation and the Fourier series expansion, the exact artificial boundary condition and a series of its approximations of the given quasilinear elliptic problem are presented. In this work, we are interested in a complex fluid-kinetic model that aims to take into account the compressibility of the droplets of the spray. The inverse scale space method arises as a limit for a penalization parameter tending to zero, while the number of The heterogenous multiscale method (HMM) is presented as a general methodology for the efficient numerical computation of problems with multiscales and multiphysics on multigrids. Specifically, we present two general solution formulae, which degenerate to the corresponding solution of the cubic NLS equation, when the quintic nonlinear term is absent. Chang, K. The fourth order $(n=2)$ version of these equations constitutes our main motivation, as it appears prominently in image processing and computer vision literature. All unauthorized attempts to access someone else's account will be logged and prosecuted. Nadzieja, Nonlinear Anal. We will show that image science demands multi-disciplinary knowledge and flexible but still robust Access to Project Euclid content from this IP address has been suspended. Employment Outlook The EULER-EUCLID MME provides outstanding professional and academic preparation to its students for a successful career in global development at the The EUCLID SG is a proud member of the IAUP. Gaussian beams are asymptotically valid high frequency solutions concen- trated on a A semi-implicit formulation of the method of spectral deferred corrections (SISDC) for ordinary differential equations with both stiff and non-stiff terms is presented. Biler, W. We deduce the ODE systems satisfied The Nordström-Vlasov system provides an interesting relativistic generalization of the Vlasov-Poisson system in the gravitational case, even though there is no direct physical application. The classical strategy of using energy estimates for higher spatial derivatives has a fundamental difficulty since formally the commutator terms Subscribe to Project Euclid Receive erratum alerts for this article Y. Forgot Password? Country Abu Dhabi Argentina Bosnia Brazil Colombia Croatia Curacao Czech Ecuador France Germany Guatemala Italy Kazakhstan Kyrgyzstan Lebanon Mexico Netherlands Peru Poland Portugal QuironSalud Romania Serbia Slovakia Slovenia South Africa Spain Sweden Switzerland Ukrainian This article presents an analysis of the dynamics of a bidimensional oscillator, which has been proposed as a simple model for the vocal fold motion at phonation. The derivation of the new equations uses a Pade(2,2) approximation of the phase velocity that arises in the linear water wave theory. Information on the WMO partnership Direct link to EUCLID's United Nations Treaty Section registration. This evolution is governed by a Fokker-Planck equation with degenerate coefficients on the boundaries, supplemented by a pair of conservation laws. When numerically solving the Liouville equation with a discontinuous potential, one faces the problem of selecting a unique, physically relevant solution across the potential barrier, and the problem of a severe time step constraint due to the CFL condition. Efendiev, V. More precisely, we are concerned with the case where these particles are immersed in a thermal bath modeled by a linear Fokker-Planck operator We present a general mathematical framework for modeling the macroscale behavior of a multiscale system using only microscale models, by formulating the effective macroscale models as dynamic models on the underlying fiber bundles. The major difference from the one-dimensional case is the motion of Note: to consult the current and official curriculum/list of courses from the EUCLID CMS database, please visit: EUCLID Available Degree Programs and follow the program link. We construct a stable and high order numerical scheme to estimate the first order spatial derivatives, or the tangent vectors in the equation. Liu and Z High frequency solutions to partial differential equations (PDEs) are notoriously difficult to simulate numerically due to the large number of grid points required to resolve the wave oscillations. If valid credentials are provided, a JSON Packet with an access_token is provided. The method is mixed and based on both a random sampling strategy and the Godunov method. Existence of optimal In this article, we discuss the question "What Level Set Methods can do for image science". Note: to consult the current and official curriculum/list of courses from the EUCLID CMS database, please visit: EUCLID Available Degree Programs and follow the program link. We present a new simple proof for the homogenization in probability. By examining the sign of fluid velocity prescribed on the boundary, initial boundary value problems with Dirichlet type boundary conditions are classified into three cases: impermeable wall problem, inflow problem and outflow problem. int Please use the button below for direct access to the Application page. Ryham, C. We show that, under appropriate assumptions on the velocity field, the large-scale, long-time behavior of the inertial particles is governed by an effective diffusion equation for the position variable alone. The system consists of a coupling of Navier-Stokes and Cahn-Hilliard equations. In this paper we investigate the stability of a range of interpolation Recently the author developed a numerical method for the multidimensional momentconstrained maximum entropy problem, which is practically capable of solving maximum entropy problems in the two-dimensional domain with moment constraints of order up to 8, in the threedimensional domain with moment constraints of order up to 6, and in the four-dimensional domain with moment constraints of order In this work, we develop a reduced-basis approach for the deficient computation of parametrized expected values, for a large number of parameter values, using the control variate method to reduce the variance. The method relies on an efficent coupling between the macroscopic and microscopic models. We also solve the linearization We perform stability analysis on the finite-difference time domain method (FDTD) when extended to incorporate local space-time adaptive mesh refinement (AMR). The gauge freedom allows us to assign simple and specific boundary conditions for both the auxiliary field and the gauge field, thus eliminating the issue of pressure boundary condition in the usual primitive variable formulation In this paper we generalize the iterated refinement method, introduced by the authors in a recent work, to a time-continuous inverse scale-space formulation. The global in time dynamics contain then also at least three different time scales for nontrivial motions of domain walls, boundaries The string method is an efficent numerical method for finding transition paths and transition rates in metastable systems. Both variational and dynamic problems are considered. The rates of pathwise convergence and convergence in expectation in Sobolev spaces are given based on the convergence rates of the spectral approximation for the stochastic convolution. Ginting, T. To deal with mixed boundary conditions, we impose geometrical constraints on the two-dimensional or three-dimensional bounded domain. Forgot Password? Country Abu Dhabi Argentina Bosnia Brazil Colombia Croatia Curacao Czech Ecuador France Germany Guatemala Italy Kazakhstan Kyrgyzstan Lebanon Mexico Netherlands Peru Poland Portugal QuironSalud Romania Serbia Slovakia Slovenia South Africa Spain Sweden Switzerland Ukrainian Euclid, Ohio 142 followers At CMS, we craft custom cabinetry & millwork with precision, innovation, and a commitment to exceeding expectations. e. Two algorithms are proposed to compute online, through a cheap reduced-basis approximation, the control variates for the computation of a large number of expectations of a functional of We study the evolution of the probability density of an asexual, one locus population under natural selection and random evolution. The argument uses some a priori bounds (uniform modulus of continuity) on the solution and the convexity and coer- civity In this paper, a spectral method is formulated as a numerical solution for the stochastic Ginzburg-Landau equation driven by space-time white noise. EUCLID is an IDB Partner. In this paper we demonstrate how concepts of white noise analysis can be used to give an explicit solution to a stochastic transport equation driven by Levy white noise. In this paper, we provide results about the long time behavior of integrodifferential equations appearing in the study of populations structured with respect to a quantitative (continuous) trait, which are submitted to selection (or competition). Hou "Multiscale Finite Element Methods for Nonlinear Problems and Their Applications," Communications in Mathematical Sciences, Commun. The We study the asymptotic behavior of the solutions of barotropic two-phase two-pressure models, with pressure relaxation, drag force and external forces. The model is capable of producing an oscillation with physiologically realistic values for the parameters. We propose an asymptotic numerical method called the Gaussian beam approach for the boundary value problem of high frequency Helmholtz equation. For large particle systems, we give a rigorous justification for the mean-field limit from the many particle Cucker We study the problem of homogenization for inertial particles moving in a time-dependent random velocity field and subject to molecular diffusion. Receive erratum alerts for this article Quick Links. Using Chapman-Enskog expansions close to the expected equilibrium, a drift-flux model with a Darcy type closure law is obtained. Our approach is based on two ideas: to write out a discrete transparent boundary condition (DTBC) using the Crank-Nicolson finite difference scheme for the governing equation, and to approximate the discrete convolution kernel of DTBC by sum-of-exponentials for a rapid recursive We prove well-posedness for the initial value problem for a vortex sheet in 3D fluids, in the presence of surface tension. You must register before attempting to log in. Two layers containing inviscid, immiscible, irrotational fluids of different densities are defined. Our result is new in that it holds even when the momentum vanishes. We show that the Willmore functional locally decreases or increases in time in the linearly stable or unstable case respectively. Furthermore it is shown that in case of spherical symmetry the system degenerates to the relativistic Vlasov-Poisson system. If you are using a third-party Content Management Software (CMS) platform you have several options on how you can build a single sign-on to the ClearVantage Web forms using our REST based web services. In cases when the macroscopic model is not explicity available or The EUCLID SG is a proud member of the IAUP. Password Show. Employment Outlook The EULER-EUCLID MBIOS-MPH provides outstanding professional and academic preparation to its students for a successful career in global health at the We present a simple proof on the formation of flocking to the Cucker-Smale system based on the explicit construction of a Lyapunov functional. We Note: to consult the current and official curriculum/list of courses from the EUCLID CMS database, please visit: EUCLID Available Degree Programs and follow the program link. The map is built iteratively, ascending the log-likelihood of the observations, through a series of steps that move the marginal distributions along a The CMS Enterprise Portal Chatbot is a computer-assisted bot that helps you find answers to questions or solve issues you are experiencing with using CMS Enterprise Portal. We introduce and discuss kinetic models for wealth distribution in a simple market economy, which are able to reproduce the salient features of the wealth distribution by including taxes to each trading process and redistributing the collected money among the population according to a given criterion. Our strategy ensures a discrete min-max principle not only for each variable but also for any number of non-trivial combinations of them, which represent control variables. Apply / Register Note: this EUCLID application system is not to be confused with the “Euclid” Portal used by the University of Edinburgh. We then perform energy estimates for the evolution equations. A finite volume scheme is developed, based on a conservative formulation of the spatially nonhomogeneous coagulation-fragmentation model. In the second case, we obtain the incompressible Euler equations with no more magnetic field left. euclid. Hebisch and T. Peskin's Immersed Boundary Method is used to model the liquid-gas interface, similar to the approach used by Unverdi and Traggvason. This problem arises in fluid mechanics codes using the Arbitrary Lagrange We show that for a particular linear Fokker-Planck operator, the explicit Chang and Cooper scheme is positive and entropy satisfying under a CFL criterion when the initial condition is positive. Our construction is fully Password : Click here if you have forgotten your password. 38 (1999), p. Communications in Mathematical Sciences. We will be recording your questions in order to improve future responses. The study of this model will probably lead to a better mathematical understanding of the class of non-linear systems consisting of hyperbolic and transport equations. They can be regarded as natural generalization of Euclidean distance. When a user browses the same site in the future, the site may extract or retrieve information stored in the cookie in order to be informed of the previous user activity. EUCLID is a proud member of the UNAI. This linear analysis explains the behavior near stationary solutions of the Cahn-Hilliard equation. Thereby we reformulate the problem on a larger domain in one higher dimension and introduce a diffuse interface region of a phase-field variable, which is defined in the whole domain. 121-131, considers as a starting point a mean-field equation for the dynamics of a gas of particles interacting via dissipative binary collisions. The ambient fluid is described by Euler-like equations, in which the transfer of momentum and energy form the droplets is taken into account, while the spray is represented by a probability density function satisfying a Vlasov-like equation. Subscribe to Project Euclid Receive erratum alerts for this article K. Our analysis gives a theoretical basis to some recent research that analyzed discrete In this note we revisit the homogenization theory of Hamilton-Jacobi and “viscous”- Hamilton-Jacobi partial differential equations with convex nonlinearities in stationary ergodic envi- ronments. We provide necessary and sufficient conditions for a convex function so that the Communications in Mathematical Sciences. In this paper, we study the existence and long-time behavior of global strong solutions to a system describing the mixture of two viscous incompressible Newtonian fluids of the same density. The SPDEs are derived by generalising the Langevin MCMC method to infinite dimensions. Appl. We consider two different asymptotic limits of the Vlasov-Maxwell system describing a quasineutral plasma with a uniform ionic background. In applications, one often must rely on approximate solution methods to describe the wave field in this regime. Zhang "Perron-Frobenius theorem for nonnegative tensors," Communications in Mathematical Sciences, Commun. We give numerical and asymptotic solutions which indicate that this singularity persists for nonmonotone solutions of the viscous Prandtl equations. Then, we deduce that the distribution given by the explicit Chang and Cooper scheme converges toward a discrete Maxwellian equilibrium. Subscribe to Project Euclid. At the same time, they give rise to an interesting This paper is devoted to a study of the asymptotic behavior of solutions of a chemotaxis model with logistic terms in multiple spatial dimensions. These limits are measures supported on zero-level-sets of the interaction potential. The surface of interest is now only implicitly given by the $1=2$-level set of this phase-field Mar 1, 2010 · We characterize the high intensity limits of minimal free energy states for interacting corpora — that is, for objects with finitely many degrees of freedom, such as articulated rods. Information on the WMO A global-in-time existence theorem for classical solutions of the Vlasov-Darwin sys- tem is given under the assumption of smallness of the initial data. For each estimate, we state the explicit dependency of constants on the wave number. In this paper it is shown that Using a rather simple model of coupled, time-dependent Ginzburg-Landau equations with two order parameters, we demonstrate that the total Hamilitonian energy of the system contains at least three levels describing point vortices, domain walls and configurations. Few programs are truly international in scope so as to fully prepare graduates for global civil service careers that will engage a wide variety of global health challenges, including malaria, HIV, drug-resistance, diet-related diseases, etc. It is important to note that the Kelvin-Helmholtz instability is present for the vortex sheet in the absence of Subscribe to Project Euclid Receive erratum alerts for this article Jean-Luc Guermond, Fabien Marpeau, Bojan Popov "A fast algorithm for solving first-order PDEs by L1-minimization," Communications in Mathematical Sciences, Commun. Gaussian beams are asymptotic solutions of linear wave equations in the high frequency regime. EUCLID (Pôle Universitaire Euclide |Euclid University): A treaty-based organization with international liaison and representative offices in New York / Washington DC, Geneva, Brussels, Berlin To retrieve your password, please enter the email address you use to access the Euclid Chemical Area. A simple extension of the model using even-powered polynomials in the damping factor is proposed, to permit the occurrence of We develop a conservative, second order accurate fully implicit discretization of ternary (three-phase) Cahn-Hilliard (CH) systems that has an associated discrete energy functional. The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336, VAT Registration Number GB 592 9507 00, and is acknowledged by the UK authorities as a “Recognised body” which has been granted degree awarding powers. Employment Outlook The EUCLID DARM provides outstanding professional and academic preparation to its students for a successful career in clinical research and teaching at We present a very efficient numerical strategy for computing contact discontinuities in traffic flow modeling. The dynamics of the string are governed by a Hamilton-Jacobi type of equation. Forgot Password? We present a new formulaiton of the incompressible Navier-Stokes equation in terms of an auxiliary field that differs from the velocity by a gauge transformation. It is applied to two We construct a model of traffic flow with sources and destinations on a roads network. It is shown that the scheme preserves positivity, total volume and global steady states. We describe a selection mechanism for the limits that is mediated by evanescent entropic contributions. After clicking on "Retrieve Password", your password will be sent to you via email. They are based on convex functions and have recently received great attention. EUCLID (Euclid University) - an intergovernmental organization under international law In this paper we prove the uniqueness of weak solutions to a model of electro-kinetic fluid which consists of a momentum equation together with transport equations of charges. We propose a way to efficiently treat the well-known transparent boundary conditions for the Schrödinger equation. The movement near the moving contact We consider the linear growth-fragmentation equation arising in the modelling of cell division or polymerisation processes. To efficiently solve the discrete system at the implicit time-level, we use a nonlinear multigrid method. Few programs are truly international in scope so as to fully prepare graduates for global civil service careers that will engage a wide variety of clinical and public health challenges, including end-of-life care, gender issues, clinical trial ethics, etc. This token along with the client_id must be put into the authorization section of the http request header for all subsequent calls. We consider the Aw-Rascle model, and the objective is to remove spurious oscillations generated for instance by the Godunov method near contact discontinuities. The system under consideration is non-strictly hyperbolic and does not admit a fully conservative form, and we establish the existence of two-parameter wave sets, rather than wave curves. Because the formulation of the problem is on a finite domain and correct, it is not difficult to design Subscribe to Project Euclid Receive erratum alerts for this article Jishan Fan, Song Jiang "Well-Posedness of an Inverse Problem of a Time-Dependent Ginzburg-Landau Model for Superconductivity," Communications in Mathematical Sciences, Commun. If you are a non-subscriber, please contact the Help Desk . The upper layer is shallow compared with the characteristic wavelength at the interface, while the bottom region’s depth is comparable to the wavelength. Information on the WMO partnership Public Health is often studied from a national-central perspective. We prove strong, mean-square convergence in systems where both fast and slow components are driven by noise, with full coupling between fast and slow components. All the functions in the model can be obtained from the real markets. For constant coefficients, we prove that the dynamics converges to the steady state with an exponential rate. The goal is to optimize the shape of quantum barriers in a quantum diode. This framework allows us to carry out seamless multiscale modeling using traditional numerical techniques. C. We analyze a class This paper, which is a sequel to Benedetto-Caglioti-Golse-Pulvirenti, Comput. Make sure to log out when your session is over, especially if you use a public access computer. The Bregman divergences are generalizations of the well known Kullback-Leibler divergence. Pearson, T. Math. Browse Search Note: to consult the current and official curriculum/list of courses from the EUCLID CMS database, please visit: EUCLID Available Degree Programs and follow the program link. Forgot password? Note: to consult the current and official curriculum/list of courses from the EUCLID CMS database, please visit: EUCLID Available Degree Programs and follow the program link. Despite the nonlinear and non-Gaussian features of the model, exact We study the convergence of the slow (or "essential") components of singularly perturbed stochastic differential systems to solutions of lower dimensional stochastic systems (the "effective", or "coarse" dynamics). Information on the WMO partnership We construct the solution of the Riemann problem for the shallow water equations with discontinuous topography. Also, restricting this closure law to permanent flows (defined as steady flows in some Lagrangian frame), we can To study the numerical solutions of quasilinear elliptic equations on unbounded domains in two or three dimensional cases, we introduce a circular or spherical artificial boundary. The algorithm implements an asymptotic semigroup for approximating the solution’s Wigner function, which was rigorously defined and derived from the Schrödinger equation by two of the authors in previous work. The algorithm proposed performs this assignment by mapping the original variables onto a jointly-Gaussian set. We use a Markov chain lattice model to represent small scale convective elements which interact with each other and with the large scale environmental variables through convective available potential energy (CAPE) and middle In this paper we outline a front-tracking method for computing the moving contact line. Employment Outlook The EUCLID DIPH and DGHHS both provide outstanding professional and academic preparation to its students for a successful career in global health policy One Time Password. Bioethics is a discipline still lacking true international and interdisciplinary experts. We examine the scope of these techniques in image science, in particular in image segmentation, and introduce some relevant level set techinquies that are potnetially useful for this class of applications. Our results also provide a unified condition on the initial states in which the exponential convergence to flocking state will occur. A nonlinear test model for filtering turbulent signals from partial observations of nonlinear slow-fast systems with multiple time scales is developed here. The neutrally stable Yee algorithm becomes extremely sensitive to perturbations introduced by the interpolation schemes employed at grid refinement interfaces. Association Management Software, Membership Management Software. The analysis can be generalized to other spectral methods for The one-dimensional motion of compressible viscous and heat-conductive fluid is investigated in the half space. In the first case, as the magnetic field is preserved in the limiting process, we obtain the so-called electron magnetohydrodynamics equations. At the equator, the Coriolis force from rotation vanishes identically so that multiple time scale dynamics for the equatorial shallow water equation naturally leads to singular limits of symmetric hyperbolic systems with fast variable coefficients. The iterated refinement procedure yields a sequence of convex variational problems, evolving toward the noisy image. This QDD model contains four space-dependent observables: The non-negative particle density of electrons, the electrostatic potential, the quantum quasi-Fermi potential and the current density. It was proposed by You and Kaveh as a model for denoising images while maintaining sharp object boundaries (edges). It has been proven that a final-value problem of the corresponding partial differential equation on a finite domain has a unique solution. We propose a strategy to perform second-order enhancement using slope-limiters for the simultaneous linear advection of several scalar variables. We introduce a new approach to deal with the numerical solution of partial differential equations on surfaces. Employment Outlook The EUCLID MPH provides outstanding professional and academic preparation to its students for a successful career in global health at the international Mar 1, 2010 · A methodology is developed to assign, from an observed sample, a joint-probability distribution to a set of continuous variables. It is readily shown that no classical or standard weak solution definition yields solvability of the problem. Of particular interest is the practically relevant case of small diffusivity, where (as in the one-dimensional case) the cell densities form plateau-like solutions for large time. This type of a propagation result has since A stochastic model for representing the missing variability in global climate models due to unresolved features of organized tropical convection is presented here. In this paper, we introduce two classes of Hamiltonian-preserving schemes for such problems. Various applications are described, including sampling paths subject to two end-point conditions (bridges) and nonlinear filter/smoothers. We first show the global existence of strong solutions in several cases. More about EUCLID and EC/BP compliance. Y. functions describing paths for cars. We propose a definition of solution at junctions, which depends on the traffic-type functions. The existence of weak solutions has been proved in P. The process starts with making a call to Euclid’s authorization service. Chatbot uses machine learning to answer your question. Enter the OTP that has been sent to your email Note: to consult the current and official curriculum/list of courses from the EUCLID CMS database, please visit: EUCLID Available Degree Programs and follow the program link. The selection of admissible waves is particularly challenging. Employment Outlook This bachelor's degree is suitable for employment but was mainly designed to prepare for further studies at the master level, either at EULER)(or EUCLID This article presents and evaluates a surface hopping algorithm for time-dependent two-level Schrödinger systems with conically intersecting eigenvalues. The basic idea is to approximate the traveling waves with a summation of Gaussian beams by the least squares algorithm. The We use the method of characteristics to prove the short-time existence of smooth solutions of the unsteady inviscid Prandtl equations, and present a simple explicit solution that forms a singularity in finite time. The algebraic method is developed to obtain new exact solutions, including stationary wave solutions and traveling wave solutions, for the cubic-quintic nonlinear Schrödinger (NLS) equation. In particular, we are interested in the motion of two-dimensional drops and bubbles on a partially wetting surface exposed to shear flows. The second order In their classical 1937 paper, Kolmogorov, Petrovsky and Piskunov proved that for a particular class of reaction-diffusion equations on the real line the solution of the initial value problem with the initial data in the form of a unit step propagates at long times with constant velocity equal to that of a certain special traveling wave solution. Several modifications and variations to the original spectral deferred corrections method by Dutt, Greengard, and Rokhlin concerning the choice of integration points and the form of the correction iteration are presented. In this paper we are interested in the finite-time stability of transition solutions of the Cahn-Hilliard equation and its connection to the Willmore functional. Information about ICCI/OIC Scholarships. TMA, 23, 1189-1209, 1994, R. Forgot Password? Password : Click here if you have forgotten your password. dfnynsow ulhv dirlelf qeslwiyc mbglbfsy tvkgc kafcu bdaf fmlmci bijj